Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations. (Q2781528)

The paper is concerned with a min-plus integral eigenvalue problem. The author proves that the unique eigenvalue of this problem depends continuously on parameters involved in the kernel defining the problem. A convergence analysis is given for the numerical method introduced by \textit{W. Chou} and \textit{R. B. Griffiths} [Ground states of one-dimensional systems using effective potentials. Phys. Rev. B 34, 6219--6234 (1986)] to compute this eigenvalue. The author illustrates obtained results in two contexts: Frenkel-Kontorova models in solid-state physics, and homogenization of Hamilton-Jacobi equations.